Add all the peels to the water and cook on a low heat for 30 minutes. Pour the broth through a sieve and express the peels well. Cut the tops of the asparagus at about 5 cm and keep them aside. Cut the rest of the asparagus into pieces.
Stew the sweet onion in the olive oil, add the drained cashew nuts and the pieces of asparagus and moisten with the asparagus broth.
Let it simmer for 10 minutes, add the lemon juice, season and mix very finely. You get the best result with a blender.
Divide the soup over the bowls.
Finish: Cut the cups of the asparagus into fine slices and sprinkle them as a decoration over the soup. Sprinkle with a few drops of olive oil.